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Distribution Modulo One and Diophantine Approximation by Yann Bugeaud

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1

Distribution modulo one

In this chapter, we give a brief account of the theory of uniform distribution modulo one. For complements, and for additional bibliographic references, the reader is directed to the monographs [232, 411].

1.1  Weyl’s criterion

In the years 1909−1910 there appeared three papers by Bohl [109], Sier-piimageski [653] and Weyl [731] devoted partly to the distribution of real sequences. A few years later, Weyl [732, 733] developed the results of these papers, giving birth to the study of uniform distribution.

DEFINITION 1.1. The sequence (xn)n≥1 of real numbers is dense modulo one if every interval of positive length included in ...

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